Skip to main content
SpringerLink
Log in

Free tensor categories

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. Y. Akutsu and M. Wadati, “Exactly solvable models and new link polynomials. I”J. Phys. Soc. Jpn.,56, 3039–3051 (1987).

    MathSciNet  Google Scholar 

  2. Y. Akutsu, T. Deguchi, and M. Wadati, “Exactly solvable models and new link polynomials. II–IV,”J. Phys. Soc. Jpn.,56, 3464–3479;57, 757–776;57, 1173–1185 (1988).

    MathSciNet  Google Scholar 

  3. M. Atiyah, “Power operations inK-theory,”Q. J. Math.,17, 165–193 (1966).

    MATH  MathSciNet  Google Scholar 

  4. M. Atiyah and D. Q. Tall, “Group representations, λ-rings and theJ-homomorphism”,Topology,8, 253–297 (1969).

    Article  MathSciNet  Google Scholar 

  5. A. A. Belavin and V. G. Drinfeld, “Solutions of classical Yang-Baxter equation,”Funkts. Anal. Prilozh.,16, No. 3, 1–30 (1982).

    MathSciNet  Google Scholar 

  6. P. Berthelot, “Generalities sur les λ-annueaux,”Lect. Notes Math.,225 (1972).

  7. N. Bourbaki,Groupes et Algebres de Lie, Hermann, Paris (1968).

    Google Scholar 

  8. N. Burroughs, “The universalR-matrix forU qsl(3) and beyond!,”Commun. Math. Phys.,127, 109–128 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  9. U. S. Chase and M. E. Sweedler, “Hopf algebras and Galois theory of rings,”Lect. Notes Math.,97, 52–83 (1982).

    Google Scholar 

  10. P. Deligne,Categories Tannakiennes, In:Grothendieck Festschrift, Vol. 2, Progress in Math., Birkhäuser,87 (1980), pp. 111–195.

  11. P. Deligne and J. Milne, “Tannakian categories, Hodge cycles, motives, and Shimura varieties,”Lect. Notes Math.,900, 101–228 (1982).

    MathSciNet  Google Scholar 

  12. A. Dold and D. Puppe, “Duality, trace and transfer,”Tr. Mat. Inst. Akad. Nauk SSSR,154, 81–97 (1983).

    MathSciNet  Google Scholar 

  13. V. G. Drinfeld, “Constant quasiclassical solutions of the quantum Yang-Baxter equation,”Dokl. Akad. Nauk SSSR,273, No. 3, 531–535 (1983).

    MATH  MathSciNet  Google Scholar 

  14. V. G. Drinfeld, “Almost commutative Hopf algebras,”Algebra Anal.,1, No. 2, 30–46 (1989).

    MathSciNet  Google Scholar 

  15. V. G. Drinfeld, “Quasihopfian algebras,”Algebra Anal.,1, No. 6, 114–148 (1989).

    MathSciNet  Google Scholar 

  16. V. G. Drinfeld, “Quasitriangular quasihopfian algebras and on one group, closely related with Gal (),”Algebra Anal.,2, No. 4, 149–181 (1990).

    MATH  MathSciNet  Google Scholar 

  17. V. G. Drinfeld, “Quantum groups” In:Proc. Int. Congr. Math. (Berkeley, 1986), Vol. 1, Am. Math. Soc., Providence (1987), pp. 798–820.

    Google Scholar 

  18. P. Freyd and D. Yetter, “Braided compact closed categories with applications to low dimensional topology,”Adv. Math.,77, 156–182 (1989).

    Article  MathSciNet  Google Scholar 

  19. D. I. Gurevich, “Poisson brackets associated with the classical Yang-Baxter equation,”Funkts. Anal. Prilozh.,23, No. 1, 68–69 (1989).

    MATH  MathSciNet  Google Scholar 

  20. D. I. Gurevich, “Yang-Baxter equation and generalization of formal Lie theory,”Dokl. Akad. Nauk SSSR,288, No. 4, 797–801 (1986).

    MATH  MathSciNet  Google Scholar 

  21. D. I. Gurevich, “Hecke symmetries and quantum determinants,”Dokl. Akad. Nauk SSSR,303, No. 3, 542–546 (1988).

    MathSciNet  Google Scholar 

  22. D. I. Gurevich, “Traces and determinants in algebras, associated with the Yang-Baxter equation,”Funkts. Anal. Prilozh.,21, No. 3, 79–80 (1987).

    MATH  MathSciNet  Google Scholar 

  23. D. I. Gurevich, “Algebraic aspects of the quantum Yang-Baxter equation,” {jtAlgebra Anal.}, {vn2}, {snNo. 4} ({dy1990}).

  24. D. I. Gurevich, “Quantum Yang-Baxter equation and a generalization of the formal Lie theory,”Rpts. Dep. Math. Univ. Stockholm, No. 24, 33–123 (1986).

    MathSciNet  Google Scholar 

  25. A. G. Izergin and V. E. Korepin, “Lattice model, related with the nonlinear Schrödinger equation,”Dokl. Akad. Nauk SSSR,259, No. 1, 76–79 (1981).

    MathSciNet  Google Scholar 

  26. A. Joyal and R. Street, “Braided monoidal categories,”Macquarie Reports,86008 (1986).

  27. G. M. Kelly, “On MacLane's conditions for natural associativities, commutativities, etc.,”J. Algebra,1, 397–402 (1964).

    Article  MATH  MathSciNet  Google Scholar 

  28. G. M. Kelly and M. L. Laplaza, “Coherence for compact closed categories,”J. Pure Appl. Algebra,19, 193–213 (1980).

    Article  MathSciNet  Google Scholar 

  29. D. Knutson, “λ-Rings and the representation theory of the symmetric groups,”Lect. Notes Math.,308 (1973).

  30. P. P. Kulish and E. K. Sklyanin, “Solution of the Yang-Baxter equation,”Zap. Nauch. Sem. LOMI,95, 129–160 (1980).

    MathSciNet  Google Scholar 

  31. A. Lichnerowich, “Les varieties de Poisson et leurs algebres de lie associe,”J. Diff. Geom.,12, No. 2 253–299 (1977).

    Google Scholar 

  32. G. Lusztig, “Modular representations and quantum groups,”Contemp. Math.,82, 59–78 (1989).

    MATH  MathSciNet  Google Scholar 

  33. V. V. Lybashenko “Vectorsymmetries,”Rpts. Dep. Math. Univ. Stockholm, No. 19, 1–77 (1987).

    Google Scholar 

  34. I. G. Macdonald,Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford (1979).

    Google Scholar 

  35. S. Majid, “Physics for algebraists: non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction,”J. Algebra,130, 17–64 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  36. S. Majid, “Representation-theoretic rank and double Hopf algebras,”Commun. Algebra,18, 3705–3712 (1990).

    MATH  MathSciNet  Google Scholar 

  37. S. Majid, “Quasitriangular Hopf algebras and the Yang-Baxter equation,”Int. J. Mod. Phys. A,5, 1–91 (1990).

    MATH  MathSciNet  Google Scholar 

  38. S. Majid, “Doubles of quasitriangular Hopf algebras,”Commun. Algebra,19, 3061–3073 (1991).

    MATH  MathSciNet  Google Scholar 

  39. S. Majid and Ya. S. Soibelman, “Rank of quantized universal enveloping algebras and modular functions,”Commun. Math. Phys.,137, 249–262 (1991).

    MathSciNet  Google Scholar 

  40. S. MacLane, “Natural associativity and commutativity,”Rice Univ. Stud.,49, 28–46 (1963).

    MATH  MathSciNet  Google Scholar 

  41. S. MacLane,Categories for Working Mathematicians, Springer-Verlag, Berlin (1971).

    Google Scholar 

  42. Yu. I. Manin, “Quantum groups and non-commutative geometry,” Preprint CRM, Montreal (1988).

  43. Yu. I. Manin, “Some remarks on Koszul algebras and quantum groups,”Ann. Inst. Fourier,37, No. 4, 191–205 (1987).

    MATH  MathSciNet  Google Scholar 

  44. A. V. Odesskiy and B. L. Feigin, “Constructions of elliptic Sklyanin algebras and quantumR-matrices,”Funkts. Anal. Prilozh.,27, No. 1, 37–45 (1993).

    Google Scholar 

  45. D. E. Radford, “A free rank 4 Hopf algebra with antipode of order 4,”Proc. Am. Math. Soc.,30, No. 1, 55–58 (1971).

    MATH  MathSciNet  Google Scholar 

  46. D. E. Radford, “On quantum Yang-Baxter operators derived from finite-dimensional Hopf algebras,”Commun. Algebra,21, 1141–1152 (1993).

    MATH  MathSciNet  Google Scholar 

  47. D. E. Radford, “On the antipode of a quasitriangular Hopf algebra”,J. Algebra,151, 1–11 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  48. N. Yu. Reshetihin, “Quasitriangular Hopf algebras, solutions of the Yang-Baxter equation, and invariants of links”,Algebra Anal.,1, No. 2, 30–47 (1989).

    Google Scholar 

  49. N. Yu. Reshetikhin and V. G. Turaev, “Ribbon graphs and their invariants derived from quantum groups”,Commun. Math. Phys.,127, 1–26 (1990).

    Article  MathSciNet  Google Scholar 

  50. N. Yu. Reshetikhin and M. A. Semenov-Tyan-Shanskii, “QuantumR-matrices and factorisation problems in quantum groups”,J. Geom. Phys.,5, 533–550 (1988).

    Article  MathSciNet  Google Scholar 

  51. A. Rosenberg and D. Zelinsky, “On Amitsur's complex”,Trans. Am. Math. Soc.,97, 327–356 (1960).

    MathSciNet  Google Scholar 

  52. R. Saavedra,Categories Tannakienes, Lect. Notes Math.,265 (1972).

  53. M. A. Semenov-Tyan-Shanskii, “What is the classicalR-matrix?”,Funkts. Anal. Prilozh.,17, No. 4, 17–33 (1983).

    MATH  MathSciNet  Google Scholar 

  54. M. E. Sweedler, “Cohomology of algebras over Hopf algebras”,Trans. Am. Math. Soc.,133, No. 1, 205–239 (1968).

    MATH  MathSciNet  Google Scholar 

  55. M. E. Sweedler,Hopf Algebras, Benjamin, New York (1969).

    Google Scholar 

  56. L. A. Tahtajan and L. D. Faddeev, “Quantum method of the inverse scattering problem and the HeisenbergXYZ-model”,Usp. Mat. Nauk,34, No. 5, 13–63 (1979).

    Google Scholar 

  57. K.-H. Ulbrich, “Galois extensions as functors of comodules”,Manusc. Math.,59, 391–397 (1987).

    MATH  MathSciNet  Google Scholar 

  58. K.-H. Ulbrich, “Fibre functors of finite-dimensional comodules”,Manusc. Math.,65, 39–46 (1989).

    MATH  MathSciNet  Google Scholar 

  59. F. Waldhausen, “AlgebraicK-theory of spaces”,Lect. Notes Math.,1126, 318–419 (1985).

    MATH  MathSciNet  Google Scholar 

  60. D. N. Yetter, “Quantum groups and representations of monoidal categories”,Math. Proc. Cambr. Philos. Soc.,108, 261–290 (1990).

    MATH  MathSciNet  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

About this article

Cite this article

Free tensor categories. J Math Sci 88, 505–519 (1998). https://doi.org/10.1007/BF02365313

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02365313

Keywords

Search

Navigation